What you are referring to is vibrato, not tremolo.
All singers use some amount of vibrato.
These days the use of strong vibrato is mostly associated with opera singing, but this was not always the case.
Vibrato helps you sing louder, and with less fatigue to the voice. Some singers learn to sing with a little vibrato or a lot, and learn how to control how much.
In the Western tradition, Vibrato is essential to singing on stage if you are unamplified -- no microphones, no PA system, no speakers.
Singing with vibrato is something that many professional singers learned to do in the era before amplification was invented and became widespread and practical (in all the years before about 1925). The idea of singing with a band without vibrato, which used to be called crooning (that was originally a derisive term) only became practical if you assumed the use of a microphone and amplification on stage, or in the case of recording the singing voice in a recording studio.
The single person most associated with developing a new style of singing based around using a microphone, without vibrato, is the great Bing Crosby (1903-1977). This kind of singing, which most pop musicians use today, didn't really exist before Bing.
If you go back and listen to some of the earliest phonograph recordings, from the 1910s and 1920s into the 1930s, in most styles of pop music around the world, you will hear that most of those singers sound somewhat like today's opera singers. By the same token, singers in Broadway musicals used a style that incorporated some degree of operatic vibrato up until the mid-1960s, because up until that time, singers in Broadway musicals sang without microphones and amplification, while accompanied by a live orchestra, just like opera singers do today. If you don't believe me, listen to original Broadway cast recordings from before the 1960s.
Vibrato is essential to operatic singing because using vibrato is part of the technique which enables a solo singer to be heard, unamplified, singing with a 40 piece orchestra in front of an audience of 2,000 people. Using vibrato also enables a singer to sing very loud and project clearly for a considerable amount of time without fatiguing or injuring the voice. You can't do that without vibrato.
I have read accounts of pop singers in the modern era who, over years of singing, damaged their vocal cords from poor technique. After they undergo corrective surgery to try to get their voice back, they have to continue with rehabilitative therapy with a voice coach. The therapy includes learning to change their singing technique by incorporating some vibrato so that they will reduce the risk of injuring their voice all over again.
Of course some pop singers who do not use vibrato develop a permanently raspy, weak voice (think Tom Petty or Bob Dylan). They like it that way, and some way or another they learn how to keep using their voice that way. It is different with every singer; they each develop their own technique and sound which works for them.